Results 21 to 30 of about 7,599 (162)
Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds [PDF]
, 2006 In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called lambda-bar. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non ...
Akutagawa, Kazuo +2 more
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Group Actions On The Sphere And Multiplicity Results For The Cr-Yamabe Equation
Bruno Pini Mathematical Analysis Seminar, 2015 We will show that the CR-Yamabe equation has several families of infinitely many changing sign solutions, each of them having different symmetries. The problem is variational but it is not Palais-Smale: using different complex group actions on the sphere,
Vittorio Martino
doaj +1 more source
Singular solutions of fractional order conformal Laplacians
, 2011 We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe ...
Gonzalez, Maria del Mar +2 more
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Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications
, 2015 In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and
Han, Yazhou, Zhu, Meijun
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The Yamabe problem on Dirichlet spaces [PDF]
, 2013 We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces
Gilles Carron +3 more
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Conformal metrics of constant scalar curvature with unbounded volumes
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract For n⩾25$n\geqslant 25$, we construct a smooth metric g∼$\tilde{g}$ on the standard n$n$‐dimensional sphere Sn$\mathbb {S}^n$ such that there exists a sequence of smooth metrics {g∼k}k∈N$\lbrace \tilde{g}_k\rbrace _{k\in \mathbb {N}}$ conformal to g∼$\tilde{g}$ where each g∼k$\tilde{g}_k$ has scalar curvature Rg∼k≡1$R_{\tilde{g}_k}\equiv 1 ...
Liuwei Gong, Yanyan Li
wiley +1 more source
Generic Properties of Critical Points of the Weyl Tensor
Advanced Nonlinear Studies, 2017 Given (M,g)${(M,g)}$, a smooth compact Riemannian n-manifold, we prove that for a generic Riemannian metric g the critical points of the function 𝒲g(ξ):=|Weylg(ξ)|g2${\mathcal{W}_{g}(\xi):=\lvert\mathrm{Weyl}_{g}(\xi)\rvert^{2}_{g}}$ with 𝒲g(ξ)≠0 ...
Micheletti Anna Maria, Pistoia Angela
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Kodaira Dimension and the Yamabe Problem [PDF]
, 1997 The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M.
LeBrun, Claude
core
Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry
, 2017 We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler-Lagrange equations of the associated energy functionals. Many solutions are given and discussed.
Cheng, Jih-Hsin +2 more
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Stability Analysis of Nondifferentiable Systems
Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.ABSTRACT Differential equations with right‐hand side functions that are not everywhere differentiable are referred to as nondifferentiable systems. This paper introduces three novel methods to address stability issues in nondifferentiable systems.
Jiwoon Sim, Tianxu Wang, Hao Wang
wiley +1 more source